A PRIORI ESTIMATES FOR THE FIFTH-ORDER MODIFIED KDV EQUATIONS IN BESOV SPACES WITH LOW REGULARITY

Mingjuan Chen; Minjie Shan

doi:10.11948/20220538

2023 Volume 13 Issue 4

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Mingjuan Chen, Minjie Shan. A PRIORI ESTIMATES FOR THE FIFTH-ORDER MODIFIED KDV EQUATIONS IN BESOV SPACES WITH LOW REGULARITY[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2315-2325. doi: 10.11948/20220538

Citation:

Mingjuan Chen, Minjie Shan. A PRIORI ESTIMATES FOR THE FIFTH-ORDER MODIFIED KDV EQUATIONS IN BESOV SPACES WITH LOW REGULARITY[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2315-2325. doi: 10.11948/20220538

A PRIORI ESTIMATES FOR THE FIFTH-ORDER MODIFIED KDV EQUATIONS IN BESOV SPACES WITH LOW REGULARITY

Mingjuan Chen^1,,
Minjie Shan^2, ,

1.
Department of Mathematics, Jinan University, Guangzhou 510632, China
2.
College of Science, Minzu University of China, Beijing 100081, China

Author Bio: Email: mjchen@jnu.edu.cn(M. Chen)
Corresponding author: Email: smj@muc.edu.cn(M. Shan)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 12001236, 12101629) and Natural Science Foundation of Guangdong Province (No. 2020A1515110494)

Abstract

Abstract

We get a priori estimates for the fifth-order modified KdV equations in Besov spaces with low regularity which cover the full subcritical range. These estimates are obtained from the power series expansion of the perturbation determinant associated to the Lax pair. More precisely, we get the global in time bounds of the $ B^s_{2,r} $ norm of the solution for $ -1/2< s < 1 $, $ 1\leq r\leq \infty $. Then we can obtain the sharp global well-posedness in $ H^s $ for $ s\geq 3/4 $, which is the minimal regularity threshold for which the well-posedness problem can be solved via the contraction principle.
- Fifth-order modified KdV equations /
- a priori estimates /
- Lax Pair /
- sharp global well-posedness
MSC: 35Q53, 35G25

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References

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